Hello - sorry I missed this thread and I even got confused by the 'cento' reference, wondering whether this should be in the Cinquecento forum!
I find in general that it helps to slacken the handbrake cable (i.e. undo the cable nuts under the car) when you fit new shoes. The shoes may not be able to self-adjust (or you may be unable to get the drums on) if the cable is too tight. Only re-tighten the handbrake once the shoes are properly self-adjusted. This also applies to rear disc brakes (e.g. Uno Turbo).
Take the drums off and check that the friction material is wearing reasonably evenly. If wearing only on the very centre of the curve, check that the drums haven't been machined too large (sometimes happens). Maximum internal diameter is 187mm.
You should probably post a picture of one of your rear brakes (with drum removed) just in case your South African Uno has a different/later design (small chance). The Punto, for example, has a different design, and I'm aware that the South African Uno was made right up until 2003-ish so may have inherited an updated design from other FIATs. Unlikely, but we have to be certain
Otherwise, you may even have the misfortune of faulty (new) shoes. I've fitted new shoes before and been unable to get them to work. It all depends on how well the spring-loaded friction washers do their job. If they shift too easily, the brakes won't work well.
Cheers,
~Alex